无限维辛群的拟自由表示
On Quasifree Representations of Infinite Dimensional Symplectic Group
摘要：
本文考虑辛群（的双重覆盖）的亚辛表示（Weil表示）的无限维推广.给定无限维CCR代数的拟自由态，利用Bogoliubov自同构的酉实现，构造了无限维辛群的投影酉表示.完整的分类，这些表示准等价获得。
英文摘要：
We consider an infinite dimensional generalization of Metaplectic representations (Weil representations) for the (double covering of) symplectic group. Given quasifree states of an infinite dimensional CCR algebra, projective unitary representations of the infinite dimensional symplectic group are constructed via unitary implementors of Bogoliubov automorphisms. Complete classification of these representations up to quasi-equivalence is obtained.
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